Veterinary Info
Budgies can and do get sick, and will need care to recover. Rather than diagnose illnesses, here's the information you need to get your bird to a vet. First, some facts:
Avian vets are widely available in the developed world, and an exam, even an emergency, rarely is over $300 USD in the US. You will need to understand that budgeting for a vet is part of
the responsibility of owning a bird. You must be prepared for that.
Not taking your bird to the vet is cruelty, especially when sick. Please do not get a budgie if you cannot afford/are unwilling to take your bird to a vet at least once a year.
Owners can be proactive in reacting to vet issues, but it's necessary to invoke them when needed. Know the signs of illness.
In the USA, the AAV has a search page for vets that are certified: https://www.aav.org/search/custom.asp?id=1803
Contact local bird stores, rescues and even normal dog/cat vets for help finding a vet.
If a certified avian vet is unavailable, contact a poultry veterinarian after searching for info about your issue. While a poultry vet is less than qualified, they may be able, with guidance of an experienced vet, make a difference in your budgie's life.
For Europe and Asia, finding a vet may be harder, but not impossible. Ask on parrot groups in your local country or call pet stores for assistance.
Do your research, recognize animal emergencies, keep basic supplies to deal with cuts, hypothermia or supportive care. Humidifiers, heating pads/heat lamps, styptic powder, and bird-safe antibiotics and antibacterials are all good to have.